We describe a variety of intriguing mode-coupling effects which can occur in a confined Bose–Einstein condensed system at finite temperature. These arise from strong interactions between a condensate fluctuation and resonances of the thermal cloud yielding strongly nonlinear behaviour. We show how these processes can be affected by altering the aspect ratio of the trap, thereby changing the relevant mode-matching conditions. We illustrate how direct driving of the thermal cloud can lead to significant shifts in the excitation spectrum for a number of modes and provide further experimental scenarios in which the dramatic behaviour observed for the m =0 mode at JILA can be repeated. Our theoretical description is based on a successful second-order finite-temperature quantum field theory which includes the full coupled dynamics of the condensate and thermal cloud and all relevant finite-size effects.
We describe a variety of intriguing mode-coupling effects which can occur in a confined Bose–Einstein condensed system at finite temperature. These arise from strong interactions between a condensate fluctuation and resonances of the thermal cloud yielding strongly nonlinear behaviour. We show how these processes can be affected by altering the aspect ratio of the trap, thereby changing the relevant mode-matching conditions. We illustrate how direct driving of the thermal cloud can lead to significant shifts in the excitation spectrum for a number of modes and provide further experimental scenarios in which the dramatic behaviour observed for the m =0 mode at JILA can be repeated. Our theoretical description is based on a successful second-order finite-temperature quantum field theory which includes the full coupled dynamics of the condensate and thermal cloud and all relevant finite-size effects.
Recent experimental observations of collective excitations of Bose condensed atomic vapours have stimulated interest in the microscopic description of the dynamics of a Bose-Einstein condensate confined in an external potential. We present a finite temperature field theory for collective excitations of trapped Bose-Einstein condensates and use a finite-temperature linear response formalism, which goes beyond the simple mean-field approximation of the Gross-Pitaevskii equation. The effect of the non-condensed thermal atoms we include using perturbation theory in a quasiparticle basis. This presents a simple scheme to understand the interaction between condensate and non-condensed atoms and enables us to include the effect the condensate has on collision dynamics. At first we limit our treatment to the case of a spatially homogeneous Bose gas. We include the effect of pair and triplet anomalous averages and thus obtain a gapless theory for the excitations of a weakly interacting system, which we can link to well known results for Landau and Beliaev damping rates. A gapless theory for trapped systems with a static thermal component follows straightforwardly. We then investigate finite temperature excitations of a condensate in a spherically symmetric harmonic trap. We avoid approximations to the density of states and thus emphasise finite size aspects of the problem. We show that excitations couple strongly to a restricted number of modes, giving rise to resonance structure in their frequency spectra. Where possible we derive energy shifts and lifetimes of excitations. For one particular mode, the breathing mode, the effects of the discreteness of the system are sufficiently pronounced that the simple picture of an energy shift and width fails. Experiments in spherical traps have recently become feasible and should be able to test our detailed quantitative predictions.
We present a finite temperature field theory for collective excitations of trapped Bose condensates which includes the dynamics of the thermal cloud. In spherical traps we show that excitations couple strongly to a small number of modes, giving resonance structure in their frequency spectra. Where possible, we derive energy shifts and lifetimes of excitations. For the l = 0 mode we show that the simple picture of a decay rate fails, which should be observable in suitable experiments. It also suggests a possible explanation for the anomalous behavior of the m = 0 mode observed in anisotropic traps.
We present a theory of the linear response of a Bose-Einstein-condensed gas to external perturbations at finite temperature. The theory developed here is the basis of a recent quantitative explanation of the measurements of condensate excitations and decay rates made at JILA [D. S. Jin et al., Phys. Rev. Lett. 78, 764 (1997)]. The formalism is based on a dynamic, number-conserving, mean-field scheme and is valid in the collisionless limit of well-defined quasiparticles. The theory is gapless, consistent with the generalized Kohn theorem for the dipole modes, and includes the time-dependent normal and anomalous averages, Beliaev and Landau processes, and all relevant finite-size effects. The important physical process where the thermal cloud is driven directly by the external perturbation is explicitly included. This is required for consistency with the dipole modes and is also needed to explain the JILA observations.
We present numerical results from a second-order quantum field theory of Bose-Einstein condensates applied to the 1997 JILA experiment [Phys. Rev. Lett. 78, 764 (1997)]]. Good agreement is found for the energies and decay rates for both the lowest-energy m=2 and m=0 modes. The anomalous behavior of the m=0 mode is due to experimental perturbation of the noncondensate. The theory is gapless and includes the coupled dynamics of the condensate and thermal cloud, the anomalous pair average, and all relevant finite size effects.
We derive a simple formula for the finite-temperature shifts of the collective excitations of a Bose-Einstein condensate. To test the validity of our treatment we apply it to explain the anomalous behavior of the ``m=2'' excitation frequency in the recent JILA experiments (D. S. Jin et al, PRL, 78 (1997) 764), where this frequency does not approach its ``noninteracting'' value at ω=2ωρ but, instead, decreases with temperature. It turns out that the effect is mainly governed by a resonance between the condensate excitation frequency and one of the quantum eigenfrequencies of the thermal cloud. Comparison of our predictions with the JILA experimental data shows a good agreement.
In this thesis we study the dynamics of dark solitons, vortices and Josephson effects, in trapped atomic Bose-Einstein condensates. We firstly demonstrate a novel, sound mediated, long-range interaction mechanism between dark solitons using the Gross-Pitaevskii equation. Then we present the effect of finite temperatures on the dynamics of vortices and Josephson effects using a generalised form of this equation, which additionally includes a source term modelling the coupling of the condensate to a fully dynamical thermal cloud, described by a quantum Boltzmann equation. The latter formalism is known as the Zaremba-Nikuni-Griffin scheme (ZNG). The sound-mediated interaction between dark solitons is such that the speed and trajectory of one soliton in a condensate confined by a harmonic trap can be significantly modified by the presence of a second soliton in the same trap. By confining the two solitons to spatially separated subregions of a double well trap, we show how this effect can be magnified. In particular we find it can be large, and therefore detectable, in experimentally relevant geometries, including high-periodicity optical lattices in which the ability of solitons to act as both absorbers and emitters of energy becomes apparent. At finite temperatures, we model the dynamics via the ZNG scheme. Firstly, we give a detailed description of the scheme for numerically solving these coupled equations including all collisional terms. Then we study the effect of a dynamical thermal cloud on vortex dynamics, in particular, focussing on the experimentally-relevant quantities of precession frequencies, decay rates and vortex core brightness. The changes in these are found to increase with increasing temperature for a pancake-shaped geometry, in particular for trapping parameters of a recent experiment of Freilich et al. (Science 329, 1182 (2010)). Particle exchanging collisions between the condensate and thermal cloud are found to be crucial in determining the rate of decay of a precessing vortex. We further show that, rotation of the thermal cloud can be a mechanism for radially translating the position of a vortex, a scenario under current investigation. Finally, we analyse the effect of finite temperatures on population dynamics in a double well atom chip experiment by LeBlanc et al. (Phys. Rev. Lett. 106, 025302 (2011)). Focussing on the coupled evolution in the absence of collisions, we find that it generates significant damping which is, however, less than that observed in the experiment. A detailed comparison in the presence of collisions is beyond the scope of this thesis.